Sensor arrangement comprising a carrier substrate and a ferroelectric layer and method for producing and using the sensor arrangement

ABSTRACT

A sensor arrangement comprises a carrier substrate and a ferroelectric layer disposed on the carrier substrate, wherein the sensor arrangement comprises means for reading the permittivity of the ferroelectric layer. The sensor arrangement is such that the ferroelectric layer is disposed in a crystalline manner on the carrier substrate. A method for producing the sensor arrangement and to use of the same is also disclosed.

BACKGROUND OF THE INVENTION

The invention relates to a sensor arrangement comprising a carriersubstrate and a ferroelectric layer, to a method for producing thesensor arrangement, and to the use of the sensor arrangement.

It is known that polarization Pi (Asm⁻²) can be induced in aninsulating, polarizable material, referred to as a dielectric, by way ofan external electric field E (Vm⁻¹). Among dielectrics, a displacementof the charge, and thus electrical polarization of the material, isbrought about in piezoelectric materials not only by external electricfields, but also by an external mechanical deformation caused bypressure, tension or torsion. The positive and negative latticecomponents are displaced as a result of the deformation so that anelectric dipole moment is created, whereby apparent charges are inducedon the surface of the outwardly neutral crystal. The termpyroelectricity collectively refers to those materials amongpiezoelectrics that have electric dipole moments even in the absence ofan external electric field, which are caused based on distortions in thecrystal lattice and the attendant displacement of charge centroids, thusbringing about electric polarization of the crystal. These substancesare thus spontaneously polarized even without an electric field.Finally, the term ferroelectricity collectively refers to thosesubstances having an electric dipole moment which change the directionof spontaneous polarization when an external electric field is applied.This phenomenon disappears above the material-dependent Curietemperature, and the material transitions into the paraelectric state.This transition is reversible, which is to say a phase transition with astructural change takes place when a drop below the Curie temperatureoccurs, and the material again transitions into the ferroelectric state.Permittivity, which is to say also the change in permittivity with thetemperature, is typically the greatest in the range of the transition. Areversible change in permittivity which is as great as possible is thusachieved in the temperature range directly above the phase transition.

The majority of ferroelectrics are oxides. The best-known ferroelectricsare ion crystals having a perovskite structure, such as BaTiO₃. Somematerials exhibit ferroelectric properties only in thin layers, forexample SrTiO₃. Ferroelectric layers are essentially used in integratedcircuits and in mobile radio communication technology.

It is known from more recent developments on ferroelectrics (R.Wördenweber, E. Hollmann, R. Ott, T. Hürtgen, Kai Keong Lee (2009).Improved ferroelectricity of strained SrTiO₃ thin films on sapphire. JElectroceram 22:363-368) to strain thin films made of ferroelectricSrTiO₃ (STO) by way of epitaxial growth and application of the latticeparameters on CeO² buffered sapphire, for example. The dielectricproperties of the strained STO were ascertained by a capacitor on thelayer.

The operating principle of pressure and bending sensors is typicallybased on the conversion of the parameter to be measured into anelectrical signal. This can take place directly or indirectly. Pressureand bending sensors can be used to directly measure pressure ordeflection and to indirectly determine other parameters, such as thetemperature, the flow or the position.

Depending on the use, the desired measuring accuracy and costs,(piezo)resistive sensors, piezoelectric sensors, inductive sensors,capacitive sensors and optical sensors are employed, for example. Often,combinations of these sensors are employed, such as in a Golay cell.

A piezoelectric pressure sensor is characterized in that a chargeseparation is induced in the crystal having polar axes by way of thepressure to be measured, and the charge separation induces an electricvoltage. This state, also known as piezoelectric effect, thus causesions to be displaced due to pressure in the interior of the crystal,forming an electric charge on the surface that is proportional to themechanically exerted force. The charge is converted into electricvoltage proportional thereto, such as by way of an amplifier. Withpiezoresistive sensors, in contrast, the resistivity of the materialschanges as long as they are subjected to a tensile load or pressureload. This effect also occurs in crystals without a polar axis, forexample in semiconductors, such as silicon.

A general problem encountered with piezoelectric pressure sensors andthe piezoresistive sensor arrangements used in strain gauges is thatthese have a comparatively complex design and are therefore costly. Thesensitivity of these sensors likewise has some room for improvement.

Another drawback is that pyroelectricity often causes interferingartifacts in the technologically relevant field of application, whichare superimposed on the piezoelectric effects that are actually ofinterest. Pressure sensors made of pyroelectric materials can indicatefalse positive signals since signals occur under heating, while nochange in pressure is present at all.

SUMMARY OF THE INVENTION

It is the object of the invention to provide a sensor arrangement thathas increased sensitivity over piezoelectric and pyroelectric sensorsfrom the prior art, while being particularly easy and cost-effective toproduce.

It is a further object of the invention to provide a method forproducing the sensor arrangement, and use thereof.

The sensor arrangement comprises a carrier substrate and a layerdisposed on the carrier substrate. The ferroelectric layer can bedisposed on the entire surface of the carrier substrate, or it can besupported by the carrier substrate only at the edge. A capacitorassembly can be disposed on the ferroelectric layer as a means forreading the permittivity of the ferroelectric layer. This assembly isused to read the electrical properties of the layer based on anoverpressure or underpressure that is normally exerted on theferroelectric layer.

As an alternative, the electronic properties can be read in anon-contact manner by way of optical measurements, such as by way ofellipsometry. In this case it is possible for the ferroelectric layer tobe supported by the carrier substrate only at the edge.

The ferroelectric layer is crystalline. If the layer is disposed on theentire surface of the carrier substrate, it is important that thecarrier substrate responds flexibly to a small pressure acting on thesensor arrangement, and is thus deflected. The thickness of the carriersubstrate should be between 1 and 500 μm.

Pressure exerted on the sensor arrangement results in compression or anexpansion of the ferroelectric layer and of the carrier substrate,resulting in a detectable change in permittivity. At room temperature,the crystal of the ferroelectric layer has a centrosymmetric orientationon the substrate, or assumes this orientation on its own, which is tosay the layer is in a dielectric state. The thickness of theferroelectric layer should be approximately 1 to 1000 nm.

The system for reading permittivity detects mechanical pressure actingnormally on the ferroelectric layer by way of a change in thepolarizability of the ferroelectric material, which occurs because ofthe transition of the layer material from the centrosymmetric latticestate to a non-centrosymmetric lattice state. Depending on thearrangement of the ferroelectric layer on the carrier substrate, anddepending on the arrangement of the read-out system on the ferroelectriclayer and the carrier substrate, the pressure exerted results incompression or expansion of the ferroelectric layer.

The sensor arrangement according to the invention is thus based on thechange in polarizability, and thus permittivity, of the ferroelectriccrystals when the crystal structure changes due to pressure application.Thus, in contrast to a piezoelectric sensor, the principle is not basedon the displacement of “positive charges in relation to negative”charges, but on the polarizability of crystals. Centrosymmetriccrystals, which are typically not ferroelectric and have only lowpermittivity, are changed into non-centrosymmetric crystals by thedeformation. This leads to an extreme increase in polarizability(permittivity), extending as far as induced ferroelectricity. Changes inpermittivity by more than one order of magnitude can be achieved with achange in the crystal lattice parameter of <1%. This advantageouslycauses the sensor arrangement to have extremely high sensitivity. Thechange in permittivity can now very easily be read capacitively or, in anon-contact manner, optically. The sensor arrangement reads outmechanical forces based on the changing polarizability of theferroelectric layer. In contrast to pyroelectric material, there arevirtually no false positive events.

Within the context of the invention, it was surprisingly found thatpolarizability of the ferroelectric layer does not only result from anepitaxially grown layer with the accompanying mechanical strain on asubstrate having deviating lattice parameters. But rather, it wasrecognized that technologically relevant, minor pressure or tensionapplied to the sensor arrangement can also result in a significantchange in permittivity of the ferroelectric layer.

Since, with appropriate selection of the ferroelectric layer, evenfractions of a change in the lattice constant, such as 10⁻⁴%, result ina measurable change in permittivity, the object is already achieved inso much as a crystalline ferroelectric layer is provided on the carriersubstrate, and the permittivity thereof is read by way of anellipsometer, for example. The optical path of the ellipsometer isdirected to the ferroelectric layer and detects the change inpermittivity.

As mentioned, the ferroelectric layer can be deposited onto a thinmembrane as the carrier substrate. Pressures in the Pa range canadvantageously be uncovered by way of the detected change inpermittivity of the ferroelectric layer. The ferroelectric layer can, ofcourse, also be disposed on the entire surface of the carrier substratewhen using an optical read-out unit, for example for reasons ofstability.

In one embodiment of the invention, a flexible foil-like or film-likecarrier substrate made of crystalline material, such as silicon orAl₂O₃, or a metal or an organic material, such as polyimide, is used asthe carrier substrate. The selection of the carrier material depends onthe particular application and the requirements of the sensor layer. Theuse of foils or films ensures a high degree of strain.

The ferroelectric material is preferably made of CaTiO₃, SrTiO₃, KTaO₃,BaTiO₃, Pb₅GeO₁₁, Eu₂(MoO₄)₃, PbTa₂O₆, KNbO₃, SrTeO₃, PbTiO₃,SrBi₂Ta₂O₉, LiTaO₃, LiNbO₃ or a combination thereof. A list of possibleferroelectrics of these is shown in Table 1. The respective transitiontemperature (Curie temperature) is indicated.

TABLE 1 Ferroelectric compounds and the transition temperatures thereofCompound T_(c) [K] CaTiO₃ (−84) SrTiO₃ (0-44) due to strain inducedphase transition 20-40 K up to room temperature KTaO₃    2.8 BaTiO₃ 396(compression) Pb₅GeO₁₁ 451 Eu₂(MoO₄)₃ 453 PbTa₂O₆ 533 KNbO₃ 708 SrTeO₃758 PbTiO₃ 763 SrBi₂Ta₂O₉ 843 LiTaO₃ 938 LiNbO₃ 1483 

Alloys made of these materials (such as (Ca,Sr)TiO₃ or (Ba,Sr)TiO₃) aswell as doped oxides of this series are likewise possible candidates forcreating the ferroelectric layer. This advantageously allows a layer, oreven a layer system, to be selected which optimally fits the particularapplication.

It is particularly advantageous if a ferroelectric layer made of amaterial having a transition temperature lower than room temperature isdisposed on the carrier substrate in such a way that pressure causestensile stress in the direction of the crystal lattice in which theelectric polarization of the crystal is measured. This advantageouslycauses the transition temperature in the crystal direction to beincreased, which also results in an increase in permittivity at roomtemperature in the crystal direction. Since the permittivity increasesvery greatly in the range before the onset of the transition toferroelectricity, an extremely sensitive sensor is thus advantageouslycreated.

It is also possible to dispose a ferroelectric material having atransition temperature higher than room temperature on the carriersubstrate in such a way that pressure causes compressive stress in thedirection of the crystal lattice in which the electric polarization ofthe crystal is measured. This advantageously causes the transitiontemperature in the crystal direction to be reduced. By analogy, therange of extremely high pressure dependency of the permittivity in thetransition region can thus again be utilized.

In this way different cases can be distinguished, which are listed inTable 2, for the arrangements of vertical and planar capacitivemeasuring devices on a membrane having a ferroelectric layer, on which apressure acts on the coated side.

TABLE 2 Examples of an arrangement of a membrane having a ferroelectriclayer with vertical or planar capacity read-out and pressure (D > 0) ortension (D < 0) engaging on the side coated with the ferroelectric. Thechange in permittivity is described for cases where the transitiontemperature T_(c) of the ferroelectric, layer is below or above roomtemperature (RT). Vertical capacitance Planar capacitance T_(c) < RT D >0 ε increases significantly ε decreases (very advantageous) D < 0 εdecreases ε increases significantly (very advantageous) T_(c) > RT D > 0ε decreases ε increases significantly (very advantageous) D < 0 εincreases significantly ε decreases (very advantageous)

The sensor arrangement particularly advantageously comprises aferroelectric material having a transition temperature greater than roomtemperature on one side of the carrier substrate, and a ferroelectricmaterial having a transition temperature lower than room temperature onthe opposite side of the carrier substrate. This advantageously allowsboth pressure and tensile stresses to be detected with high sensitivity.

A method for producing the sensor arrangement according to the inventionprovides for a ferroelectric material to be disposed on a crystallinemanner on the carrier substrate by way of physical vapor deposition(PVD), chemical vapor deposition (CVD) or other deposition methods(chemical solution deposition (CSD), electrophoretic deposition (EPD)and the like), and for at least one capacitor assembly to be disposed onthe ferroelectric material, the assembly detects the mechanical forceexerted by way of the change in permittivity of the mechanicallydeformed layer. As an alternative, the permittivity can be read in anon-contact manner, for example optically by way of ellipsometry.

The described sensor arrangements are advantageously used as pressure orbending sensors. A mechanical force is exerted on the sensor arrangementin a pressure or bending sensor. This results in a reversible change inthe polarizability of the ferroelectric layer and is read in a mannercorresponding to the capacitor system or in a non-contact manner. Afterthe force subsides, the polarizability of the ferroelectric layer isreturned to the starting condition again.

The sensors according to the invention can be used particularlyadvantageously in the following fields of application:

As bending and strain sensors having extremely high sensitivity, formeasuring the absolute value of bending or expansion, and for thedirectional-dependent and local measurement of bending or expansion withsimple electronic read-out. Fields of applications include pressuremeasurement, overpressure control or (through-)flow measurements ofgases or liquids; position determination and positioners, intouchscreens, for analog measuring transducers (such as temperaturemeasurement in a Golay cell), and as switches, for example fortriggering safety systems such as airbags, all the way to intelligentcircuits.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: shows a principle of the sensor arrangement according to theinvention;

FIG. 2: shows a schematic illustration (sectional view) of sensorarrangements according to the invention comprising a carrier substrateand a ferroelectric layer with optical reading;

FIG. 3: shows a schematic illustration (sectional view) of sensorarrangements according to the invention comprising a carrier substrateand a ferroelectric layer with capacitive reading; and

FIGS. 4a, b : show top views of different capacitive reading capacitors.

Identical reference numerals in the figures denote identical components.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the principle of the sensor arrangement according to theinvention. Polarizability is a measure of the displaceability of apositive charge relative to a negative charge when an external electricfield is applied. The higher the polarizability is, the more easily adipole moment can be induced by an electric field. Polarizability iscomposed of an electric portion (displacement of the electron cloudrelative to the nuclei) and an ionic portion (displacement of positiveions relative to negative ions). Ionic polarizability provides thegreatest contribution to permittivity. Moreover, the ionic contributionis highly dependent on the crystal structure, in particular on crystalsymmetry. It generally holds true that centrosymmetric crystals cannotbe ferroelectric (FIG. 1, center).

According to the invention, the crystal structure, and also the crystalsymmetry, is changed by (uniaxial or biaxial) pressure, see FIG. 1, leftand right. This brings about a change in the polarizability P of thecrystals. According to the invention, the greatest change is to beexpected when a non-centrosymmetric structure (left and right) iscreated from a centrosymmetric structure (center). Here, a ferroelectricstate is created from a dielectric state by lattice distortion. Thiscauses enormous changes in permittivity. In the case of epitaxial,monocrystalline layers, the inventor measured an increase from ∈≈300 to∈≈5000 in a perovskite (ABO₃ structure) with a change in the latticeconstant of only approximately 1%. It is the inventive assumption of theinvention that similar modifications in permittivity can also beachieved mechanically with pressure changes in the Pa range. The bottomportion of the figure in each case shows an arrangement of the layer onthe carrier for the different states. The ferroelectric layer 2 isdisposed on the carrier substrate 1. The thick arrows on the left andright at the bottom of FIG. 1 indicate the overpressure D (left) andunderpressure D (right) acting on the arrangement. Depending on thearrangement of the ferroelectric layer, this results in compression orexpansion of the crystal structure in the layer plane. This compressionor expansion is then partially compensated for by the opposite expansionor compression perpendicular to the layer plane. The effect can takeplace in an exactly reversed manner by additionally arranging the layerunder the carrier.

It generally holds true that a positive or negative pressure normal tothe membrane causes a compression or expansion in the layer plane of theferroelectric layer, with simultaneous compensation normal to the layerplane.

P in the upper portion of FIG. 1 indicates the direction ofpolarizability of the crystal when, as is shown in the bottom portion,an overpressure or underpressure acts on the ferroelectric layer.

FIG. 2 shows the pressure sensor with optical reading (ellipsometry),consisting of a light source L, polarizer P, analyzer A and detector DE.The following cases are shown:

a) Ferroelectric layer on the side of the membrane facing the pressure(D>0). Alternatively the membrane can be dispensed with, and theferroelectric layer can be designed as the membrane.

b) Ferroelectric layer under the side of the membrane facing thepressure (D>0). Alternatively the membrane can be dispensed with, andthe ferroelectric layer can be designed as the membrane.

c) Membrane coated on both sides with a ferroelectric sensor layer isread optically on both sides. Alternatively the membrane can bedispensed with, and the ferroelectric layer can be designed as themembrane.

The dotted lines in the figures for the membrane 21 and for the detectorlayer 22 indicate the states of the same deflected from the neutralposition after pressure load D.

The figures schematically show the basic elements of the pressure ortensile sensor with optical reading, comprising the membrane holder 23of the membrane 21 and the sensor layer 22. The dotted line indicatesthe deflected state of the membrane with the sensor layer based on apressure D. The dotted arrows describe the optical beam for opticalreading, such as by way of ellipsometry. For microscopic measurements,the membrane can have lateral dimensions of several micrometers toseveral centimeters for non-spatially-resolved highly sensitivemeasurements. The thickness of the membrane 21 can be selected in therange of 10 μm. The thickness of the sensor layer is typically 200 nm.Here, it is also conceivable to operate without the carrier substrate21, for example when using a sufficiently thick sensor layer (2 μm), thedeflection of which causes the top side and bottom side of the crystalstructure to be strained opposite from each other and only one of thetwo surfaces to be captured by the optical reading.

FIG. 3 shows the pressure sensor with capacitive reading by way of aplate capacitor assembly for determining the normal polarization of theferroelectric layer. The plate capacitor comprises electrodes 27 and 28and the electronically connected reading electronics 26. The followingcases are shown:

a) Ferroelectric layer on the side of the membrane facing the pressure(D>0), comprising an electrode pair 27 including only the ferroelectriclayer, and an electrode pair 28 including the ferroelectric layer andthe membrane.

b) Ferroelectric layer under the side of the membrane facing thepressure (D>0), comprising an electrode pair 27 including only theferroelectric layer, and an electrode pair 28 including theferroelectric layer and the membrane.

c) Double-sided reading of a membrane coated on both sides withferroelectric sensor layers by way of two electrode pairs 27 a, 27 bincluding only the ferroelectric layer, wherein one electrode pairmeasures on the top layer, while the second electrode pair measures onthe bottom layer.

FIG. 3 shows a schematic illustration of the sensor arrangement in asectional view, composed of a carrier, which here is a membrane 21 forpressure measurements, a ferroelectric perovskite layer 22 serving asthe detector layer, an annular holder 23 serving as the carriersubstrate for the layers 21, 22, as in FIG. 2, however with capacitivereading electrodes 27 a, 27 b, 28 a, 28 b and capacitive readingelectronics 25, 26.

The change in permittivity can thus also be read capacitively, as isshown in the figures. A parallel plate capacitor assembly can beselected for this purpose. The polarizability of the detector layer 22is determined normal to the carrier substrate 21 or to the membraneplane.

Arrow D, in turn, indicates the pressure on the carrier substrate 21 andthe detector layer 22. A parallel plate capacitor 27 a, 27 b is shown tothe left of arrow D, in which the electrodes include only the detectorlayer; to the right thereof a parallel plate capacitor 28 a, 28 b isshown, in which the two electrodes comprise the membrane or carriersubstrate 21 and the sensor layer as the ferroelectric layer 22. Sincethe dielectric properties of the carrier substrate and of theferroelectric sensor layer are measured, in this case on the right, itmust be ensured here that the permittivity, and more particularly thechange in permittivity during deflection, is negligibly small. Bothstructures are possible in combination, as shown, or individually.

The parallel plates 27 a, 27 b and 28 a, 28 b form the capacitances C:

$\begin{matrix}{{C = {ɛ_{o}ɛ\;\frac{A}{d}}},} & \left( {{equation}\mspace{14mu} 1} \right)\end{matrix}$wherein ∈₀=8.85·10⁻¹² [As/Vm] denotes the electric field constant, ∈denotes the dielectric constant or permittivity of the medium betweenthe plates, and A and d denote the surface and distance of the plates,respectively. Thus, in general the following applies to thesearrangements and to the planar arrangements of the electrodes on thedetector layer:C∝∈.  (equation 2),

The higher sensitivities are essentially achieved by extending theeffective gap using interdigital structures 30 a, 30 b.

FIG. 4 shows top views (in (a) and (b)) of different capacitive readingcapacitors for determining the planar polarizability, which is to saythe permittivity in the layer plane. The electrode pairs are applied tothe ferroelectric sensor layer in each case. Again, the membrane servingas the carrier can be dispensed with.

a) Planar parallel plate assembly in standard design.

b) Planar interdigital structure, with which higher resolutions onsmaller measuring surfaces are achieved.

c) Different measuring arrangements in a transverse view show thepossible positioning of the planar electrode pairs.

From the left:

A planar electrode pair is disposed on the ferroelectric layer, which inturn is disposed on the membrane, and determines the planarexpansion/compression of the ferroelectric layer below the membrane.

A planar electrode pair is disposed under the ferroelectric layer, whichin turn is disposed under the membrane, and determines the planarexpansion/compression of the ferroelectric layer above the membrane.Here, the expansion and compression in the layers above and below themembrane can be determined simultaneously.

Planar structures are advantageously used to measure the permittivity ofthe detector layer 22 in the layer plane. Depending on the goal of theapplication, different capacitor structures can thus be used, such asstandard structures composed of two strips 29 a, 29 b disposed inparallel, at a minimal distance, or interdigital structures 30 a, 30 bhaving increased capacitance. Here, the permittivity, and thus thedeflection in different directions, can be determined separately by wayof the orientation of the capacitor structures. The planar arrangementsdetermine the permittivity only in the direction that is predefined bythe electrodes. This arrangement is thus suited for measuring thedeflection of the membrane with the sensor layer in a directionpredefined by the electrode structure. In this arrangement, the sensorthus also functions as a deflection sensor. Due to the differentarrangement of the capacitor structures, the deflection of the membranewith the sensor layer can now be evidenced in different directions.

In general, the local change in deflection can be determined byminiaturization of the capacitor structures. Moreover, dynamic locallyresolved processes can be captured (for example, for touchscreens) byway of temporal data acquisition.

The sensor arrangement is produced as follows.

An Si carrier is used as the carrier material 21, in which a region isthinned to approximately 2 to 5 μm by way of etching, so that a thin,flexible membrane is created on a round surface measuring approximately10 mm in diameter. The wafer is now provided with a thin crystallineferroelectric layer made of SrTiO₃ on the planar side by way ofmagnetron cathode sputtering. The layer thickness of the SrTiO₃ layer isapproximately 50 nm. An electrode pair, including feed lines for thecapacitive measurement, is now applied to this layer using thin-filmtechnology by way of a lift-off method and gold evaporation. Theelectrodes for the capacitive measurement of the permittivity arelocated on the membrane, and the feed lines from the electrodes lead tocontacts of the measuring electronics 25, 26 outside the membrane. Theelectrodes are composed of rectangles measuring 8 mm×1 mm, the longedges of which are disposed parallel to each other and form a gap of 2μm.

The Si wafer is applied to a Golay cell in a vacuum-tight manner. Usingthe feed lines located outside the membrane, the capacitance of thecapacitive system on the membrane is now determined by way of an LCmeter. Changes in the temperature of the Golay cell cause a pressurechange in the interior of the cell, leading to a deflection of the Simembrane 21. The change in permittivity of SrTiO₃ effected by thedeflection of the membrane now causes a change in capacitance. Thechange in the temperature of the Golay cell is thus converted into aneasy-to-measure change in capacitance.

A deflection of the carrier layer 21 and of the detector layer 22 due toa pressure change D thus always affects the capacitor assembly 27 a, 27b, including the measuring electronics 25 and 28 a, 28 b and 26, as wellas 29 a, 29 b and 30 a, 30 b. Capacitances from the pF range to the μFrange can thus be read this way.

The invention claimed is:
 1. A sensor arrangement comprising: a carriersubstrate; a ferroelectric layer disposed in a crystalline manner on thecarrier substrate and forming a crystalline lattice, the ferroelectriclayer disposed relative to the carrier substrate in a configuration bywhich mechanical distortion of the carrier substrate causes a mechanicaldistortion of the crystalline lattice and a change in polarizability ofcrystals among the crystalline lattice, wherein said change inpolarizability of the crystals is accompanied by a change inpermittivity of the ferroelectric layer; a plurality of planar platesconfigured relative to the ferroelectric layer to form one or morecapacitive reading capacitors having a capacitance that is proportionalto said permittivity of the ferroelectric layer, a first one capacitorof said one or more capacitive reading capacitors comprising a firstplanar electrode extending over a region of the ferroelectric layer thatis less than an entire face of the ferroelectric layer.
 2. The sensorarrangement according to claim 1, wherein the carrier substrate is aflexible carrier substrate.
 3. A sensor arrangement according to claim1, wherein the carrier substrate comprises silicon or Al₂O₃ or polyimideor a metal.
 4. The sensor arrangement according to claim 1, comprising aferroelectric material made of CaTiO₃, SrTiO₃, KTaO₃, BaTiO₃, PbsGeO₁₁,Eu₂(MoO₄)₃, PbTa₂O₆, KNbO₃, SrTeO₃, PbTiO₃, SrBi₂Ta₂O₉, LiTaO₃, LiNbO₃or a combination of these materials.
 5. A sensor arrangement accordingclaim 1, wherein the ferroelectric layer comprises a material having atransition temperature lower than room temperature, so that a pressureresults in tensile stress on the crystal lattice of the ferroelectriclayer.
 6. A sensor arrangement according claim 1, comprising aferroelectric material having a transition temperature higher than roomtemperature is disposed on the carrier substrate, so that a pressureresults in compressive stress on the crystal lattice.
 7. A sensorarrangement according to claim 1, comprising a ferroelectric materialhaving a transition temperature higher than room temperature and beingdisposed on one side of the carrier substrate, and a ferroelectricmaterial having a transition temperature lower than room temperature andbeing disposed on the opposite side of the carrier substrate.
 8. Amethod for producing a sensor arrangement according to claim 1,comprising disposing a ferroelectric material in a crystalline manner onthe carrier substrate by way of physical vapor deposition, chemicalvapor deposition, chemical solution deposition or electrophoreticdeposition.
 9. A method of sensing with the sensor arrangement accordingto claim 1 configured as a pressure or bending sensor, comprising:receiving a mechanical force that is normally exerted on the sensorarrangement; undergoing in response to said mechanical force areversible change in the polarizability of the ferroelectric layer; andafter the force subsides, undergoing a return of the polarizability ofthe ferroelectric layer to the starting condition again.
 10. The methodof sensing according to claim 9, further comprising measuring thepressure at the transition temperature of the ferroelectric layer. 11.The sensor arrangement according to claim 1, wherein said first planarelectrode is located on a first surface of the ferroeletric layeropposite the carrier substrate, and wherein said first one capacitorfurther comprises a second planar electrode located at an interfacebetween the carrier substrate and a second face of the ferroelectriclayer, said second planar electrode encompassing an area less than anentirety of said interface.
 12. The sensor arrangement according toclaim 1, wherein said first planar electrode is located on a firstsurface of the ferroeletric layer opposite the carrier substrate, andwherein said first one capacitor further comprises a second planarelectrode located on a first surface of the carrier substrate oppositethe ferroelectric layer, said second planar electrode encompassing anarea less than an entirety of said first surface of the carriersubstrate.
 13. The sensor arrangement according to claim 11, whereinsaid one or more capacitive reading capacitors comprises a secondcapacitor comprising: a third planar electrode extending over a secondregion of first surface of the ferroelectric layer that is less than anentirety of said first surface of the ferroelectric layer, and a fourthplanar electrode located on a first surface of the carrier substrateopposite the interface, said second planar electrode encompassing anarea less than an entirety of said first surface of the carriersubstrate.
 14. The sensor arrangement according to claim 1, wherein theplurality of planar plates are configured relative to the ferroelectriclayer to form a plurality of said capacitive reading capacitors, whereinsaid first capacitive reading capacitor and a second capacitive readingcapacitor among said plurality of capacitive reading capacitors areconfigured respectively at a different orientation; wherein said firstcapacitive reading capacitor detects a corresponding first componentdirection of a change in polarizability of the crystals based on ameasured capacitance at said first capacitive reading capacitor; andwherein said second capacitive reading capacitor detects a correspondingsecond component direction of a change in polarizability of the crystalsbased on a measured capacitance at said second capacitive readingcapacitor.
 15. The sensor arrangement according to claim 1, wherein theferroelectric layer is a first ferroelectric layer disposed on one sideof the carrier substrate; further comprising a second ferroelectriclayer disposed as a crystalline structure on another side of the carriersubstrate and forming a second crystalline lattice, the secondferroelectric layer disposed relative to the carrier substrate in aconfiguration by which mechanical distortion of the carrier substratecauses a mechanical distortion of the second crystalline lattice and achange in polarizability of crystals among the second crystallinelattice, wherein said change in polarizability of the crystals among thesecond crystalline lattice is accompanied by a change in permittivity ofthe second ferroelectric layer; wherein the first ferroelectric layerhas a transition temperature between a dielectric state and aferroelectric state that is less than room temperature and the secondferroelectric layer has its transition temperature between thedielectric state and the ferroelectric state that is greater than roomtemperature so that a measurement sensitivity of the sensor arrangementfor a first direction of mechanical distortion of the carrier substrateis greater at said first ferroelectric layer than at said secondferroelectric layer, and the measurement sensitivity of the sensorarrangement for a second direction of mechanical distortion of thecarrier substrate is greater at said second ferroelectric layer than atsaid first ferroelectric layer.
 16. A sensor that detects mechanicalpressure acting on a membrane, the sensor comprising: a carriersubstrate; a ferroelectric layer disposed in a crystalline manner on thecarrier substrate and forming a crystalline lattice, the carriersubstrate and ferroelectric layer forming the membrane; and a pluralityof planar plates configured relative to the ferroelectric layer to formone or more capacitive reading capacitors having a capacitance that isproportional to said permittivity of the ferroelectric layer, whereinthe ferroelectric layer is disposed relative to the carrier substrate ina configuration by which mechanical distortion of the carrier substratecauses a mechanical distortion of the crystalline lattice and a changein polarizability of crystals among the crystalline lattice, whereinsaid change in polarizability of the crystals is accompanied by a changein permittivity of the ferroelectric layer; wherein a pair of planarplates among said plurality of planar plates, along with a portion ofthe membrane therebetween, forms a first capacitive reading capacitor, acapacitance of the first capacitive reading capacitor being a measure ofsaid mechanical pressure, said capacitance varying according to saidmechanical pressure.
 17. The sensor of claim 16, wherein said pair ofplanar plates comprise a first planar electrode extending over a firstface of the ferroelectric layer that is less than an entirety of saidfirst face of the ferroelectric layer, and a second planar electrodelocated at an interface between the carrier substrate and a second faceof the ferroelectric layer, said second planar electrode encompassing anarea less than an entirety of said interface.
 18. The sensor of claim16, wherein said pair of planar plates comprise a first planar electrodeextending over a first face of the ferroelectric layer that is less thanan entirety of said first face of the ferroelectric layer; and a secondplanar electrode located on a first surface of the carrier substrateopposite the ferroelectric layer, said second planar electrodeencompassing an area less than an entirety of said first surface of thecarrier substrate.
 19. The sensor of claim 16, wherein said plurality ofplanar plates comprises a second pair of planar plates configuredrelative to the ferroelectric layer to form a second capacitive readingcapacitor, wherein said first capacitive reading capacitor and saidsecond capacitive reading capacitor are configured to have a differingorientation; wherein said first capacitive reading capacitor detects acorresponding first component direction of a change in polarizability ofthe crystals based on a measured capacitance at said first capacitivereading capacitor; and wherein said second capacitive reading capacitordetects a corresponding second component direction of the change inpolarizability of the crystals based on a measured capacitance at saidsecond capacitive reading capacitor.
 20. The sensor of claim 16, whereinthe ferroelectric layer is a first ferroelectric layer disposed on onesurface of the carrier substrate; further comprising a secondferroelectric layer disposed as a crystalline structure on anothersurface of the carrier substrate and forming a second crystallinelattice, the second ferroelectric layer disposed relative to the carriersubstrate in a configuration by which mechanical distortion of thecarrier substrate causes a mechanical distortion of the secondcrystalline lattice and a change in polarizability of crystals among thesecond crystalline lattice, wherein said change in polarizability of thecrystals among the second crystalline lattice is accompanied by a changein permittivity of the second ferroelectric layer; wherein the firstferroelectric layer has a transition temperature between a dielectricstate and a ferroelectric state that is less than room temperature andthe second ferroelectric layer has its transition temperature betweenthe dielectric state and the ferroelectric state that is greater thanroom temperature, so that sensitivity of said measure of mechanicalpressure for a first direction of mechanical distortion of the carriersubstrate is greater at said first ferroelectric layer than at saidsecond ferroelectric layer, and sensitivity of said measure ofmechanical pressure for a second direction of mechanical distortion ofthe carrier substrate is greater at said second ferroelectric layer thanat said first ferroelectric layer.
 21. The sensor of claim 16, whereinthe carrier substrate comprises silicon or Al₂O₃ or polyimide or ametal.
 22. The sensor of claim 16, wherein the ferroelectric layercomprises a ferroelectric material made of CaTiO₃, SrTiO₃, KTaO₃,BaTiO₃, PbsGeO₁₁, Eu₂(MoO₄)₃, PbTa₂O₆, KNbO₃, SrTeO₃, PbTiO₃,SrBi₂Ta₂O₉, LiTaO₃, LiNbO₃ or a combination of these materials.